University of Cambridge > > Isaac Newton Institute Seminar Series > Singularities of Burgers’ equation in the complex plane

Singularities of Burgers’ equation in the complex plane

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact nobody.

AR2W02 - Mathematics of beyond all-orders phenomena

Following on from previous work, we analyse solutions to Burgers’ equation in the complex plane, concentrating on the dynamics of the complex singularities and their relationship to the solution on the real line. We use a variety of tools, including matched asymptotic expansions, exponential asymptotics, exact solutions, steepest descents and rational approximations. The small-time limit highlights how infinitely many singularities are born at $t = 0$ and how they orientate themselves to lie increasingly close to anti-Stokes lines in the far-field of the inner problem. This inner problem also reveals whether or not the closest singularity to the real axis moves toward the axis or away. Further analysis characterises the motion of the singularities for intermediate and late times. While Burgers’ equation has an exact solution, we deliberately apply a mix of techniques in our analysis in an attempt to develop methodology that can be applied to other nonlinear partial differential equations that do not.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity